Fast Learning in Reproducing Kernel Krein Spaces via Signed Measures

• URL: http://arxiv.org/abs/2006.00247v3
• Date: Tue, 9 Feb 2021 14:20:54 GMT
• Title: Fast Learning in Reproducing Kernel Krein Spaces via Signed Measures
• Authors: Fanghui Liu, Xiaolin Huang, Yingyi Chen, and Johan A.K. Suykens
• Abstract summary: We cast this question as a distribution view by introducing the emphsigned measure A series of non-PD kernels can be associated with the linear combination of specific finite Borel measures. Specifically, this solution is also computationally implementable in practice to scale non-PD kernels in large sample cases.
• Score: 31.986482149142503
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we attempt to solve a long-lasting open question for non-positive definite (non-PD) kernels in machine learning community: can a given non-PD kernel be decomposed into the difference of two PD kernels (termed as positive decomposition)? We cast this question as a distribution view by introducing the \emph{signed measure}, which transforms positive decomposition to measure decomposition: a series of non-PD kernels can be associated with the linear combination of specific finite Borel measures. In this manner, our distribution-based framework provides a sufficient and necessary condition to answer this open question. Specifically, this solution is also computationally implementable in practice to scale non-PD kernels in large sample cases, which allows us to devise the first random features algorithm to obtain an unbiased estimator. Experimental results on several benchmark datasets verify the effectiveness of our algorithm over the existing methods.

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